I live in Jackson and I think the Alpine Slide (although fun) might be a bit much for the 1 & 3 year old... I would instead suggest Storyland (a mile from the Lodge at Jackson)- it is inexpensive, clean and fun for ages 1-9. There is also Santa's Village which is great but it is about an hour drive from Jackson.

The folks who own the Lodge are really great - with kids, check out the Red Fox or the Shannon Door for dinner. Both a few hundred yards from the Lodge, inexpensive and kid friendly!

If you want a babysitter for one of the evenings, I have an 18 year old who is great with kids and in need of cash (so I don't have to keep paying for her gas) :-)